Estimate the sum by rounding the mixed numbers to the nearest whole numbers. \( 13 \frac{2}{3}+22 \frac{1}{5}+9 \frac{11}{15} \) (A) 44 (B) 45 (D) 46 (D) 47

First, let's round each mixed number to the nearest whole number. For \(13 \frac{2}{3}\), rounding to the nearest whole number gives us 14. For \(22 \frac{1}{5}\), we round it down to 22, and for \(9 \frac{11}{15}\), we also round it up to 10. Adding these rounded numbers together: \(14 + 22 + 10 = 46\). So, the estimated sum is 46, which corresponds to option (D)!